Hank Aaron put up so many outrageous numbers over the course of his career that it makes 715 feel almost like an afterthought.

Aaron was a 25-time All-Star — and that's not a typo: from 1959-1962, he played in both of the All-Star games held each summer back then. He was a .305 lifetime hitter. He had more than 3,700 hits, including a major-league record 1,477 for extra bases. He drove in 2,297 runs (another record). He won a World Series ring; won a couple of batting titles; and, perhaps most incredibly, he still holds the record of 17 consecutive seasons with 150 or more hits.

Aaron spoke with LIFE.com about some of the players — teammates as well as rivals — who made his playing days so satisfying, and so much fun, for so many years. Now 79 years old (b. Feb 5, 1934), Mr. Aaron is as gracious as he is insightful in his praise of his friends and foes. Talking with him was a straight-up honor.

Finally: That's a pretty cool old-school multiple-exposure shot of Aaron's 715th up there, right? You can even see the two kids who ran on to the field to congratulate the man as he rounded the bases — and startled the hell out of him. Anyone's who ever seen footage of that night knows the look that crossed Aaron's face when they hove into view: Oh, what the fuck is THIS now?

And even then, he maintained his cool. Amazing.

Ben Cosgrove is the editor of LIFE.com. Picture This is his weekly (and occasionally more frequent) feature for The Stacks.